有限元Ritz-Volterra投影的超收敛性质及其应用

The Superconvergence Properties of Finite Element Ritz-Volterra Projection and Applications

本文研究有限元Ritz－Volterra投影的超收敛性质．利用一种新型的Green函数，证明了该投影具有与有限元Ritz投影相平行的函数和导数逼近的超收敛性质．这些结果被应用于抛物型积分微分方程和Sobolev方程的半离散有限元近似．

The purpose of this paper is to study the superconvergence properties of Ritz-Volterra projection defined on the finite element spaces. By means of a new type of Green functions, we prove that those delicate superconvergence properties of function and gradient approximoltions shared by the Ritz projection also hold for the Ritz-Volterra projection. Then, these results are applied to the semidiscrete finite element approximation to parabolic integro-differential equation and Sobolev equation.